The Novikov-Boone-Britton Theorem proves the undecidability of the word problem for these mathematical objects.  The number of subsets fixed by their elements is proportional to the number of orbits according to Burnside's Lemma. If "p to the n" is the largest power of prime
The Novikov-Boone-Britton Theorem proves the undecidability of the word problem for these mathematical objects.  The number of subsets fixed by their elements is proportional to the number of orbits according to Burnside's Lemma. If "p to the n" is the largest power of prime p that divides the order of one of these objects, then it contains a sub-object of size "p to the n" according to (*) Sylow's Theorem. A sub-object of one of these objects must have an order that divides the order of the original object according to Lagrange's Theorem. These objects are defined as monoids which include inverse elements, and their namesake axioms include closure and the presence of an identity element. These objects consist of a set and a single binary operation, and are called Abelian when they commute. For 10 points, name these mathematical objects studied in abstract algebra that are more general than a ring.
The Novikov-Boone-Britton Theorem proves the undecidability of the word problem for these mathematical objects.  
{groups}